Optimized composite flexbeam for helicopter tail rotors

ABSTRACT

An optimized composite flexbeam (10) having a pitch region (PR) which includes a core laminate (50) of unidirectional fiberglass material (U F ), and face laminates (52) of unidirectional graphite material (U G ) bonded to mating surfaces (50 M ) defined by the core laminate (50). The core laminate (50) and face laminates define an aspect ratio which is greater than or equal to 10 and define chamfered edge surfaces (54 S ). Each chamfered edge surface (54 S ) defines a critical acute angle α with respect to the flapwise bending neutral axis (X A ) of the pitch region (PR) and defines a lateral edge (54 E ) disposed a vertical distance X from the flapwise bending neutral axis (X A ). The critical acute angle α is between about 14 degrees to about 22 degrees and the vertical distance X is about 12.5% to about 37.5% of the pitch region thickness dimension (T PR ). The optimized composite flexbeam (10) further includes an inboard transition region (ITR) having a first transition subregion (ITR-1) and a second transition subregion (ITR-2). The second transition subregion (ITR-2) defines a width conic and a critical width transition subregion (Cr wt ). Furthermore, the first and second inboard transition regions (ITR-1, ITR-2) are composed of a combination of unidirectional and off-axis composite materials (U, O) wherein the off-axis composite material (O) defines a percentage %O of off-axis composite material (O) and wherein the percentage %O in the critical transition subregion (CR wt ) is defined by an optimized curve (100).

TECHNICAL FIELD

This invention is directed to bearingless rotors for helicopters, and,more particularly, to an optimized composite flexbeam for helicoptertail rotor assemblies.

BACKGROUND OF THE INVENTION

Helicopter rotor designs are increasingly utilizing a flexiblestructural member, commonly termed a "flexbeam" or "flexbeam connector",for retention of a helicopter rotor blade to a torque drive hub member.Basic operational constraints of rotary wing flight impose substantialfunctional complexity upon the rotor flexbeam necessitated by the needto accurately control the multi-directional displacement of the rotorblades, i.e., flapwise and edgewise bending, and torsional or pitchchange motions. As such, these configurations are termed "BearinglessRotors" inasmuch as they replace antiquated bearing element rotors whichaccommodate motion by hinge or journal type bearings at the rotor bladeroot end. The flexbeam, which is typically comprised of fiber reinforcedresin matrix materials, reduces the weight, complexity, and maintenanceof the rotor assembly while, furthermore, improving the reliability anddamage tolerance thereof.

In the context of a helicopter tail rotor application, the flexbeam isinterposed between and secured in combination with a central torquedrive hub member and a tail rotor blade assembly. The flexbeam istypically enveloped by a torque tube assembly which is mounted incombination with the outboard end of the flexbeam and which is operativeto impart pitch motion to the flexbeam/tail rotor blade assembly. Suchpitch motion is imparted to the torque tube by means of a star-shapedpitch beam which is disposed in combination with the inboard end of thetorque tube such that linear displacement of the pitch beam effectsrotational displacement of the torque tube.

The design of a flexbeam typically involves iteratively examining amultiplicity of interrelated design criteria in view of the chosencomposite matrix materials, fiber orientation thereof, design envelopeand manufacturing constraints. Such interrelated design criteriainclude, inter alia, requirements for the flexbeam to 1) accommodate apredefined spectrum of loads and motions, e.g., 30,000-35,000 lbs ofcentrifugal, 4,000 lbs of thrust, ±18 degrees of pitch motion, +5degrees of flap motion, etc. 2) maintain steady and vibratorystresses/strains, .i.e., axial, bending, buckling, and torsional, belowthe maximum static and fatigue stress/strain allowables of the selectedmaterial, 3) maintain input control loads, i.e., loads acting on/throughthe pitch control rods, to acceptable levels, 4) produce desiredstiffness attributes to avoid resonant instabilities, 5) occupy aminimal design envelope and 6) facilitate low cost manufacturing. Itwill be appreciated that many of the above design criteria arecompeting, i.e., are non-consonant with each other, hence, an iterativetrade-study must be performed to optimize the flexbeam.

To accommodate the loads and motions, the flexbeam is typicallysegregated into various regions wherein each region is designed toperform a principle function. Generally, the flexbeam will comprise atleast five such regions including a hub attachment region, an inboardtransition region, a pitch region, an outboard transition region and ablade attachment region. As will be discussed hereinbelow, certainregions of the flexbeam, i.e., the inboard transition and pitch regions,are more highly loaded and more vigorously exercised than other regions,and, accordingly, are more critical to the design of the flexbeam.

The hub attachment region is typically characterized by a thickenedrectangular cross-section which is interposed between and mounted toupper and lower clevis plates of a central hub retention member.Functionally, the hub attachment region is principally designed forreacting/transferring centrifugal and bending moment loads, e.g.,flapwise and edgewise, acting on the flexbeam. Insofar as the hubattachment region is rigidly affixed to the hub retention member,flexural motion is not a design requirement.

The inboard transition region, also referred to as the flap-flexureregion, is principally designed for reacting flapwise and edgewisebending moment loads and for effecting a width and thickness transitionbetween the hub attachment and pitch regions. With regard to the latter,it is typically desirable for such width and thickness transitions to beeffected over a relatively short spanwise length so as to minimize theoverall length of the flexbeam and maximize the effective length of thepitch region. Furthermore, for tail rotor applications, it is typicallydesirable to minimize the effective hinge offset, i.e., the distancefrom the rotational axis of the tail rotor assembly to the "effective"flapping hinge defined by the flexural/stiffness characteristics of theflexbeam. Reduction of the hinge offset diminishes the hub momentsacting on the hub attachment region/hub retention member. This istypically achieved by minimizing the width and thickness of the inboardtransition region so as to soften the flexbeam, and, consequently, shiftthe hinge offset to an inboardmost position. Limitations to theseobjectives relate to high stress concentrations, e.g., interlaminarshear, along the free edges of the flexbeam, which stress concentrationscan result in delamination or splintering of the flexbeam.

The pitch region is principally designed to accommodate the requisitepitch motion of the rotor blade assembly, minimize the control loadsrequired to effect pitch control, provide the requisite edgewisebuckling stability, and define the chordwise frequency of theflexbeam/rotor blade system. Generally, for tail rotor applications, thepitch region must accommodate about 14 to about 18 degrees of pitchmotion which is imparted by means of the torque tube assembly.Concomitantly, the pitch region must be torsionally soft so as tominimize control loads. It will be appreciated that the powerrequirements to produce the forces required to twist the flexbeam are afunction of the torsional stiffness of the flexbeam pitch region.Furthermore, the pitch region must have the requisite edgewise stiffnessto withstand steady and vibratory inplane bending moments induced byaerodynamic drag and/or Coriolis forces.

In addition to the load and motion requirements, the pitch regiondominates the 1st chordwise frequency attributes of the flexbeam. Thatis, the flexbeam pitch region must have a characteristic edgewisestiffness which produces a desired chordwise frequency response. Forexample, in a tail rotor application, it is desirable to effect a 1stchordwise frequency of about 1.7 cycles/rev. to (i) eliminate therequirement for lead-lag dampers and (ii) avoid load amplification atthe resonant harmonic frequencies of the rotor blade/flexbeam assembly.With regard to the former, it is generally desirable to stiffen theflexbeam pitch region so as to effect a frequency response above 1.0cycles/rev., thereby reducing edgewise blade motion, and, consequently,eliminating the requirement for lead-lag damping apparatus. With regardto the latter, it is typically necessary to effect a 1st chordwisefrequency between harmonic frequencies, corresponding to 1.0, 2.0, or3.0 cycles/rev. etc., so as to avoid resonant instability due to loadamplification. While 1st chordwise frequencies between 2.0 and 3.0cycles/rev. meet the above criteria, such dynamic characteristicsnecessitate yet higher stiffness values and, consequently, generatehigher control loads.

The outboard transition and blade attachment regions are principallyloaded in tension, i.e., due to centrifugal loads, and are lightlyloaded as compared to the inboard flexbeam regions. Furthermore,flexural motion is not a design requirement insofar as the inboardtransition and pitch regions are principally responsible foraccommodating flapwise, edgewise and pitch excursions of theflexbeam/rotor blade assembly. The outboard transition region alsoaccommodates a width and thickness transition between the pitch andblade attachment regions, however, due to relatively low stresses, i.e.,approximately 1/3 the stress levels of the inboard transition region,such width and thickness transitions can occur rapidly without inducinglarge interlaminar shear stresses.

Prior art flexbeams address the problems associated with delamination orsplintering in the inboard transition region by incorporating anexternal composite overwrap (see Beno et al. U.S. Pat. No. 4,898,515) oredge caps (see Schmaling et al. U.S. Pat. No. 5,431,538) disposed overthe free edges to strengthen the composite flexbeam. Furthermore, theinboard transition regions disclosed in these references employ a linearwidth transition wherein the width transition angle, i.e., the angledefined by the lateral edges of the pitch and inboard transitionregions, is shallow, e.g., between about 1.5 to about 3 degrees. Suchshallow width transition angle, in combination with the overwrap or edgecaps, effects the necessary reduction in interlaminar stress to obviatesplintering or delamination of the composite flexbeam. While theteachings therein provide the requisite structural solutions, it will beappreciated that the weight and manufacturing complexity of the flexbeamis adversely impacted. Furthermore, it will be appreciated that thespanwise length of the inboard transition region must increase to effecta linear transition having a shallow transition angle. Such increasedlength has the disadvantageous effect of increasing the overall spanwiselength of the flexbeam or, conversely, decreasing the effective lengthof the pitch region. Such decreased effective length complicates theability to establish the requisite 1st chordwise frequency response andincreases the twist rate requirements in the pitch region. With regardto the latter, the increased twist rate induces yet higherstresses/strains, thereby further complicating the design of the pitchregion.

The structural and functional design complexities of the pitch regionhave been addressed by multi-lobed and cruciform cross-sectionalconfigurations such as those described in Noehern et al. U.S. Pat. No.4,746,272, and in the Schmaling '538 patent. Generally, these flexbeamdesigns produce a 1st chordwise frequency response of about 0.7cycles/rev. and are not, therefore, applicable to tail rotorapplications which, as discussed above, benefit from a higher chordwisefrequency of about 1.7 cycles/rev. Assuming, arguendo, that such pitchsections could be appropriately sized to increase the chordwisefrequency response, other structural and manufacturing difficultiesarise due to the configuration and fabrication techniques employedtherein.

More specifically, the Noehren '272 patent discloses a pitch regionhaving multiple lobes defined by a plurality of machined grooves. Themultiple-lobes provide buckling stability while the machined groovesreduce the torsional stiffness of the flexbeam. It will be appreciatedthat the machined grooves induce high stress concentrations which canlead to premature failure of the flexbeam. Furthermore, the machiningoperation must be highly controlled to achieve the desiredcross-sectional configuration and, consequently, fabrication costs areadversely impacted.

The Schmaling '538 patent discloses a pitch region comprised of a basefiberglass structure and supplemental graphite ribs disposed on eitherside thereof, which graphite ribs are substantially narrower than thebase fiberglass structure to form a cruciform-shaped cross-sectionalconfiguration. The combination of materials and cross-sectionalconfiguration provides a low torsional stiffness, a low 1st chordwisefrequency, and improved edgewise buckling stability. While the pitchsection described therein provides solutions to these and other designdifficulties, the cross-sectional configuration is, nonetheless,difficult and costly to fabricate. More specifically, a highly accuratepress mold is employed for fabricating the flexbeam, which press moldmust provide compaction pressure in both the thickness and widthdirections of the flexbeam to produce a high quality composite laminate.Such press molding apparatus typically requires precise set-up andcontrolled thickness lay-up of the composite material to ensure thatuniform pressure is applied to the composite-lay-up.

The success of this molding process is dependent upon a variety ofindependent variables such as the degree of bulk variation from onecomposite ply to another, the accuracy of the press mold, i.e., itsability to apply controlled compaction pressure and temperature, and, ofcourse, operator proficiency. Furthermore, it will be appreciated thatsuch press mold apparatus, which typically comprises rigid matched metalmolds, is incapable of providing compaction pressure in both the lateraland transverse directions, i.e., the width and thickness directions ofthe composite flexbeam. Should any of the above variables be askew, thequality of the composite laminate may be compromised, and accordingly,the flexbeam may require rework or may be scrapped depending upon thedegree of distortion or malformation.

A need therefore exists for a composite flexbeam, particularly adaptedfor a helicopter tail rotor assembly, which is design optimized forreducing interlaminar shear stresses, providing the requisite bucklingstability, satisfying 1st chordwise frequency requirements, andminimizing the torsional stiffness of the composite flexbeam while,furthermore, facilitating the manufacture thereof.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an optimizedcomposite flexbeam having a unique configuration and combination ofmaterials for reducing interlaminar shear stresses while meeting avariety of interrelated flexbeam design criteria.

It is another object of the present invention to provide such anoptimized composite flexbeam which facilitates manufacturing processescapable of producing a high quality composite laminate.

These and other objects of the invention are achieved by an optimizedcomposite flexbeam having a plurality of adjoining regions including ahub attachment region, a blade attachment region, an inboard transitionregion adjoining the blade attachment region, an outboard transitionregion adjoining the blade attachment region, and a pitch regiondisposed between and adjoining the inboard and outboard transitionregions.

The pitch region includes a core laminate of unidirectional fiberglassmaterial, and face laminates of unidirectional graphite material bondedto mating surfaces defined by the core laminate. The core laminatedefines lateral surfaces which further define a pitch region widthdimension, and the face laminates define face surfaces which furtherdefine a pitch region thickness dimension. The width and thicknessdimensions define an aspect ratio which is greater than or equal to 10.Furthermore, the core and face laminates define a chamfered edgeconfiguration having chamfered edge surfaces, wherein each chamferededge surface defines a critical acute angle with respect to the flapwisebending neutral axis of the pitch region and defines a lateral edgedisposed a vertical distance from the flapwise bending neutral axis. Thecritical acute angle is preferably between about 14 degrees to about 22degrees and the vertical distance is preferably about 12.5% to about37.5% of the pitch region thickness dimension.

The inboard transition region includes a first transition subregiondefined by a thickness transition and a second transition subregiondefined by a width and thickness transition. The second transitionsubregion defines a width conic and a critical width transitionsubregion. The critical width transition subregion corresponds to conicslope angles, defined by the width conic, of between 0 degrees to about10 degrees. Furthermore, the first and second inboard transition regionsare composed of a combination of unidirectional and off-axis compositematerials wherein the off-axis composite material defines a percentageof off-axis composite material and wherein the percentage in thecritical transition subregion is defined by an optimized curve.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present invention and the attendantfeatures and advantages thereof may be had by reference to the followingdetailed description of the invention when considered in conjunctionwith the following drawings wherein:

FIG. 1 is a partially exploded perspective view of a helicopter tailrotor assembly including the optimized composite flexbeam of the presentinvention;

FIGS. 2a and 2b are plan and side views of the optimized compositeflexbeam for depicting various adjoining regions thereof including a hubattachment region, an inboard transition region, a pitch attachmentregion, an outboard transition region, and a blade attachment region;

FIG. 3 is a cross-sectional view taken substantially along line 3--3 ofFIG. 2a for revealing the internal construction and cross-sectionalconfiguration of the pitch region;

FIGS. 4 and 5 are representative partial perspective views of a baselinepitch region and the pitch region of the optimized composite flexbeam,respectively, for comparing and contrasting the edge configurationsthereof;

FIG. 6 is a graph of the interlaminar shear stress/in-plane shear stressratios vs. normalized edge distance for the baseline pitch region andpitch region of the optimized composite flexbeam;

FIG. 7a depicts a representative sectional view of an alternateembodiment of the optimized composite flexbeam wherein the pitch regionis shown to include a central zone of alternating unidirectionalgraphite and fiberglass composite plies;

FIG. 7b is an enlarged view of FIG. 7a wherein the unidirectionalgraphite and fiberglass plies are shown in greater detail;

FIG. 8 is a schematic partially broken-away side view of the pitch,inboard transition and hub attachment regions of the optimized flexbeamfor illustrating, inter alia, the composite ply lay-up and thicknessvariations therein;

FIG. 9a is a partial plan view of the pitch, inboard transition and hubattachment regions of the optimized composite flexbeam for illustrating,inter alia, a width conic defined by lateral surfaces of the inboardtransition region;

FIG. 9b is a detailed broken view of the width conic and a criticalwidth transition subregion defined by a range of conic slope angles;

FIG. 10 is a graph of the percent off-axis composite material in thecritical width transition subregion as a function of the conic slopeangle;

FIG. 11 depicts a schematic partially broken-away plan view of a priorart composite flexbeam overlaying the optimized composite flexbeam ofthe present invention for comparing and contrasting the various featuresthereof;

FIG. 12 is a schematic partially broken-away side view of the pitch,outboard transition and blade attachment regions of the optimizedflexbeam for illustrating, inter alia, the composite ply lay-up andthickness variations therein;

FIG. 13 is a partial plan view of the pitch, outboard transition andblade attachment regions of the optimized composite flexbeam;

FIG. 14 is a partially broken-away plan view of a mold assembly used forfabricating the optimized composite flexbeam;

FIG. 15 is a cross-sectional view taken substantially along line 15--15of FIG. 14.

BEST MODE FOR CARRYING OUT THE INVENTION

Referring now to the drawings wherein like reference characters identifycorresponding or similar elements throughout the several views, FIG. 1depicts a partially exploded perspective view of a bearinglesshelicopter tail rotor assembly 2. The tail rotor assembly 2 includes acentral hub retention member 4 for driving a plurality of tail rotorblades 6 about an axis of rotation 8. More specifically, an optimizedcomposite flexbeam 10 according to the present invention is interposedbetween and secured in combination with the hub retention member 4 andeach tail rotor blade 6. Connecting bolts 12 secure the outboard end10_(OE) of the optimized flexbeam 10 to the respective tail rotor blade6 and connecting bolts 16 affix the inboard end 1_(IE) of the flexbeam10 to upper and lower clevis arms 4a and 4b, respectively, of the hubretention member 4.

Each optimized flexbeam 10 is enveloped by a torque tube 20 which ismounted in combination with the outboard end 10_(OE) of the flexbeam 10via the same connecting bolts 12 employed for effecting theflexbeam/tail rotor blade attachment. The torque tube 20 is,furthermore, articulately mounted at an inboard end 20_(IE) by means ofan elastomeric bearing assembly 22, also referred to as a snubberbearing assembly, which performs the functions of centering the torquetube 20 about the optimized flexbeam 10, accommodating relative pitch,flap and lead-lag motion between the torque tube 20 and the optimizedflexbeam 10, and for transferring pitch control and other loadstherebetween. Such snubber bearing assemblies 22 are wellknown in theart and are further described in U.S. Pat. Nos. 5,092,738, and5,499,903.

The torque tube 20 is operative to impart pitch motion to thecorresponding tail rotor blade assembly 6, which pitch motion, inaddition to other blade excursions, is accommodated by the torsionalelasticity of the optimized flexbeam 10. More specifically, pitch motionis imparted to the torque tube 20 by means of a star-shaped pitch beam24 which is disposed in combination with the inboard end 20_(IE) of eachtorque tube 20 via a pitch control rod 26 and pitch horn fitting 28. Inoperation, linear displacement of the pitch beam 24 effects rotationaldisplacement of each torque tube 20, which, in turn, imparts pitchcontrol inputs to the corresponding tail rotor blade 6.

Before discussing the optimized composite flexbeam 10 in detail, itshould be understood that the described embodiment is based upon a tailrotor assembly having certain predefined load and motion requirements.Each optimized flexbeam 10 described herein a) reacts 33,000 lbs(146,784 N) of centrifugal load generated by each tail rotor bladeassembly, b) reacts steady and vibratory flapwise bending loads(produced by rotor blade thrust) of about 15,000 in-lbs (1,695 N-m)steady and about +38,000 in-lbs (4,293 N-m) vibratory, c) transferssteady and vibratory edgewise bending loads (associated with rotortorque) of about 8,000 in-lbs (904 N-m) steady and about +21,000 in-lbs(2,373 N-m) vibratory, d) accommodates +5 degrees of out-of-plane(flapwise) motion, e) accommodates +18 degrees of pitch motion whilemaintaining pitch control loads below +200 lbs, f) produces a hub momentconstant of 1,250 ft-lbs/deg. (97,106 N-m/rad.), and g) produces a 1stchordwise frequency of about 1.7 cycles/rev. It will be appreciated thatvarious modifications to the optimized composite flexbeam 10, e.g., thelength, cross-sectional area, severity of width and/or thicknesstransition etc., may be made within the spirit and scope of theinvention.

Additional variables which influence the configuration of the optimizedflexbeam 10 include the selection of materials and the mechanicalproperties thereof, e.g., the elastic modulus of the fiberreinforcement, the fiber orientation thereof, the shear modulus of theresin matrix, and the stress and strain allowables of the compositematerial etc. For the described embodiment, the optimized compositeflexbeam 10 comprises fiber reinforced resin matrix materials whereinthe fibrous reinforcement includes both graphite and fiberglass fibersand wherein the resin matrix is a toughened epoxy matrix. Morespecifically, the optimized flexbeam 10 includes a plurality of graphiteor fiberglass composite plies which are stacked and arranged to form alaminated composite structure having anisotropic/orthotropic strengthproperties, i.e., a structure having predefined stiffness propertiesalong orthogonal axes as a function of the orientation of the fiberreinforcement. Such strength properties are effected by a selectcombination of unidirectional and/or off-axis composite material. In thecontext used herein, unidirectional material is characterized by itsfiber reinforcement being substantially parallel to the longitudinalaxis 10_(L) of the optimized composite flexbeam 10, i.e., about 0degrees relative thereto, and off-axis composite material ischaracterized by its fiber orientation being about +45 degrees or -45degrees relative to the longitudinal axis 10_(L). Furthermore, referenceto unidirectional and/or off-axis "material", "fiber", or "plies" willbe used interchangeably to denote the directional strength of thecomposite laminate. While the relative placement and fiber orientationof the resulting graphite/fiberglass composite laminate are, inter alia,essential features of the invention, it should be understood that othercomposite matrix materials may be employed provided that such materialshave similar mechanical properties, e.g., elastic and shear moduli,stress/strain allowables, etc.

In FIGS. 2a and 2b, the optimized composite flexbeam 10 according to thepresent invention is segmented into various adjoining regions for thepurpose of identifying particular structural and functional attributesthereof. More specifically, the composite flexbeam 10 comprises: a hubattachment region HAR, a blade attachment region BAR, a pitch region PR,and inboard and outboard transition regions, ITR and OTR, respectively.The following discussion addresses the primary functions, structuralattributes and composite construction of each region. While a primaryfunction of the optimized flexbeam 10, and, accordingly, all regionsthereof, is the reaction of blade-induced centrifugal loads, theprinciple functions of each region will be described in terms of uniquefunctions which are specific thereto.

The hub attachment region HAR is configured to accommodate securement ofthe composite flexbeam 10 in combination with the hub retention memberand, more specifically, includes a spaced pattern of mounting apertures40 for effecting the bolted connection illustrated in FIG. 1.Functionally, the hub attachment region HAR is primarily designed totransfer flexbeam moments, i.e., flapwise and edgewise bending moments,and centrifugal loads to the hub retention member. Insofar as the hubattachment region HAR is rigidly affixed to the hub retention member,significant flexural motion is not a design requirement. The hubattachment region HAR is characterized by a constant width and thicknessdimension, W_(HAR) and T_(HAR), respectively, and is principallycomprised of a 50/50 admixture of off-axis and unidirectional graphitematerial, though, a small percentage of fiberglass material (bothunidirectional and off-axis material) is present to facilitate thedesired composite lay-up in the pitch region and inboard transitionregions PR, ITR. The off-axis and unidirectional composite materialproduces an anisotropic composite laminate which provides optimumtransfer of flexbeam loads into the connecting bolts.

The blade attachment region BAR is configured to secure the optimizedcomposite flexbeam 10 to each tail rotor blade assembly and,concomitantly, to the torque tube 20, by means of mounting apertures 42for effecting the outboard bolted attachment of FIG. 1. Functionally,the blade attachment region BAR is principally designed to reactcentrifugal loads and transfer torque to the rotor blade assembly.Insofar as bending moments are small, the blade attachment region BAR islightly loaded as compared to other regions of the optimized compositeflexbeam 10. The characteristics regarding its composite construction,e.g., width and thickness W_(BAR), T_(BAR), admixture of off-axis andunidirectional composite material, etc., are the same as for those ofthe hub attachment region HAR.

The pitch region PR is situated between the hub and blade attachmentregions HAR, BAR and is structurally configured to (i) accommodate therequisite pitch motion of the tail rotor blade assembly i.e., theelastic torsional displacement due to pitch inputs, (ii) minimize thecontrol loads required to effect pitch control, (iii) provide therequisite buckling stability, and (iv) define the 1st chordwisefrequency response of the flexbeam/tail rotor blade system. Morespecifically, the pitch region PR incorporates a select combination ofcomposite material and a unique cross-sectional configuration to satisfythe aforementioned design requirements.

The pitch region PR is characterized by a substantially constantcross-sectional geometry along its length L_(PR). In FIG. 3, the pitchregion comprises a core laminate 50 of unidirectional fiberglassmaterial and face laminates 52 of unidirectional graphite materialbonded to upper and lower mating surfaces 50_(M) defined by the corelaminate 50. Preferably, the face laminates 52 of graphite materialextend substantially the full width dimension W_(PR) of the pitch regiondefined by the lateral surfaces 50_(L) of the core laminates 50.Furthermore, the width dimension W_(PR), in combination with the pitchregion thickness dimension T_(PR) measured between the upper and lowerface surfaces 52_(F) of the face laminates 52, define a width tothickness ratio W_(PR) /T_(PR), hereinafter referred to as the aspectratio of the pitch region 34. The aspect ratio is preferably greaterthan or equal to 10 and, more preferably, between a range of about 10 toabout 20. For the described embodiment, the aspect ratio is about 16.2.The import of the such composite materials and the aspect ratio will bediscussed in subsequent paragraphs.

The unidirectional orientation of the fiberglass and graphite materialof the core and face laminates 50, 52, respectively, produces a laminatehaving orthogonal properties wherein the torsional stiffness isprincipally a function of the shear moduli (G) of the resin matrices andwherein the axial or bending stiffness is principally a function of theelastic modulus (E) of the fibers. Consequently, the pitch region PR ischaracterized by a low torsional stiffness about the longitudinal axis10L of the composite flexbeam due to the relatively low shear moduli (G)of the resin matrices and a high axial stiffness due to the high elasticmodulus (E_(G)) Of the unidirectional fibers, and particularly, thegraphite fibers. With regard to the former, the low torsional stiffnessproduces a torsionally compliant pitch region PR which minimizes controlloads, i.e., reduces the forces required to twist the optimized flexbeamabout the longitudinal axis 10_(L). With regard to the latter, andreferring to the encircled regions R_(C), the graphite fibers thereinare distally spaced from the flapwise and bending neutral axes X_(A),Y_(A) and, accordingly, are highly effective in providing both flapwiseand edgewise bending stiffness. Such high flapwise and edgewise bendingstiffness provides in-plane buckling stability about the edgewisebending neutral axis Y_(A).

While the graphite face laminates 52, and, in particular, the edgewisestiffness component thereof, contributes, in large part, to the 1stchordwise frequency response of the optimized flexbeam 10, the lowelastic modulus (E) of the fiberglass core laminate 50 serves toameliorate the stiffening effects of the graphite face laminates 52.More specifically, the percentage of fiberglass material in the pitchregion PR is preferably between a range of about 50% to about 70% of thetotal material, and, more preferably, is between about 50% to about 60%of the total material. For the described embodiment, the percentage offiberglass is about 59%. Insofar as the width dimension W_(PR) of thelaminates 50, 52 is essentially equal, the ratio of the core thicknessdimension T_(C) to the pitch region thickness dimension T_(PR) alsodefines the percentage of fiberglass material. Such material orthickness range, in combination with the above described aspect ratio,produces a 1st chordwise frequency response of about 1.7 cycles/rev.Material or thickness ranges below the prescribed range, i.e., 50%,produces a 1st chordwise frequency response above about 1.9 cycles/revwhich, as discussed in the Background of the Invention, may result inresonant instability if positioned at or near a load amplification valuee.g., 2.0 cycles/rev or, alternatively, produce high control loads ifpositioned between load amplification values, e.g., between 2.0 and 3.0cycles/rev. The upper end of the material or thickness percentage range,i.e., 70%, is limited by the in-plane fatigue shear stress allowable ofthe fiberglass material.

In addition to the combination of materials, material thickness andaspect ratio described above, the pitch region PR is characterized bychamfered edge surfaces 54_(S) to reduce interlaminar shear stressesalong the lateral surfaces 50_(L) of the core laminates. Suchinterlaminar shear stresses are introduced therein as a result of theaspect ratio of the pitch region PR and the maximum in-plane shearstresses developed along the face surfaces 52_(F) of the graphite facelaminates 52.

In FIGS. 4 and 5, a baseline pitch region PR_(BL) having a right-anglededge configuration RA_(E) is compared and contrasted with the optimizedpitch region PR of the present invention. In FIG. 4 a representativepartial perspective view of the baseline pitch region PR_(BL) isdepicted wherein maximum in-plane and interlaminar shear stresses areproduced at points A and B, respectively. Point A is disposed along theface surfaces 52_(FBL) of the baseline pitch region PR_(BL) and iscolinearly aligned with the edgewise bending neutral axis Y_(ABL). PointB is disposed along the lateral surfaces 50_(LBL) of the baseline pitchregion PR_(BL) and is colinearly aligned with the flapwise bendingneutral axis X_(ABL). The rectangular baseline pitch region PR_(BL)incorporates core and face laminates, 50_(BL) and 52_(BL), respectively,of the same material, material thickness', and aspect ratio as definedearlier for the pitch region PR of the optimized flexbeam 10. Applyingthe same pitch region requirements as described above, the maximumin-plane shear stresses τ_(IP) ^(A) developed at point A along the facesurfaces 52_(FBL) are found by expression 1.0:

    τ.sub.IP.sup.A ≈(θ/L)GT                  (1.0)

wherein θ is the pitch prorate, L is the length of the pitch regionPR_(BL), G is the shear moduli of the laminates (dominated by the resinmatrices) and T is the total thickness. While the terms L, G, and T areself-explanatory, the pitch prorate is the maximum pitch angle θ forwhich a material, based on the usage spectrum thereof, is capable ofwithstanding multiple cyclic torsional loads without degrading itsstructural properties (analogous to the endurance strength of amaterial).

The interlaminar shear stresses τ_(IL) ^(B) at point B developed alongthe lateral surfaces 50_(LBL) may be found using St. Venant's torsiontheory for determining torsional shear stresses in a rectangularcross-section having substantially orthotropic properties, i.e., whereinthe shear modulus G about the torsional axis is uniform. Insofar as thetorsional shear moduli G of the unidirectional fiberglass and graphitematerial are substantially equal, due to the resin matrices common toboth, this theory is applicable to both the baseline and optimized pitchregions PR_(BL), PR. In the context used herein substantially equalshear moduli means within a range of about +10% According to St. Venant,rectangular cross-sections of the type described above produce maximumtorsional shear stresses along orthogonal sides which are proportionalto each other based on the width and thickness of the rectangularcross-section, i.e., the aspect ratio thereof. For rectangularcross-sections having an aspect ratio between 10 and 20, the followingexpression defines the relationship between the maximum in-plane andmaximum interlaminar (out-of-plane) shear stresses.

    τ.sub.IL ≈0.73τ.sub.IP                     (2.0)

wherein τ_(IP) is the maximum in-plane shear stress, and τ_(IL) is themaximum interlaminar shear stress.

From expressions 1.0 and 2.0, therefore, it will be appreciated that fora rectangular-shaped orthotropic structure (aspect ratio between 10 and20) wherein the maximum in-plane shear stress τ_(IP) ^(A) at point A is4,000 lbs/in² (27.6* 10⁶ N/m²), the maximum interlaminar shear stressτ_(IP) ^(B) at point B will be 2,968 lbs/in² (20.5* 10⁶ N/m²). Insofaras the maximum fatigue allowable interlaminar shear stress forunidirectional fiberglass material is about 2,000 psi (13.8* 10⁶ N/m²),it will be appreciated that the baseline pitch region PR_(BL) does notprovide an interlaminar shear stress solution for the cited example.

In FIG. 5, the optimized pitch region PR provides an interlaminar shearstress solution by chamfering the edges of the pitch region PR suchthat, for a given aspect ratio and maximum in-plane shear stress, eachchamfered edge surface 54_(S) defines a critical acute angle α withrespect to the flapwise bending neutral axis X_(A) and such that alateral edge 54_(E) of each chamfered edge surface 54_(S) is disposed avertical distance X from the flapwise bending neutral axis X_(A).Preferably, the critical acute angle α is within a range of about 14 toabout 22 degrees, and, more preferably, within a range of about 16 toabout 2 degrees. Furthermore, the vertical distance X is preferablywithin a range about 1/8 to about 3/8ths of the pitch region thicknessdimension T_(PR).

To precisely define a critical angle α suitable for a particularapplication, an inscribed circle analysis may be employed wherein thelateral and chamfered edge surfaces 50_(L), 54_(S) are disposedtangentially to an inscribed circle IN_(CIR) which defines the bounds ofthe chamfered edge configuration CH_(E). More specifically, the criticalangle α may be determined by calculating a value for the maximumdiameter D_(MAX) of the inscribed. circle IN_(CIR), and selecting avalue of X within the prescribed range. As will be apparent by thefollowing analysis, the maximum interlaminar shear stress at point B isa function of the maximum diameter D_(MAX) of the inscribed circleIN_(CIR) and is proportional to the maximum in-plane shear stress atpoint A which is a function of the pitch region thickness dimensionT_(PR). As such, the inscribed circle IN_(CIR) may be tailored indiameter to ensure that the interlaminar shear stresses in the corelaminate 50 of unidirectional fiberglass are within acceptable levels.

The maximum diameter D_(MAX) is derived from expressions 1.0 and 2.0above and is based on the maximum fatigue shear stress allowables ofgraphite and fiberglass and on the pitch prorates thereof. Thederivation of the maximum diameter D_(MAX) of the inscribed circleIN_(CIR) is as follows:

    τ.sub.(Gr.F.ALLOW) ≈(θ.sub.PG /L)GT.sub.PR (3.0)

    τ.sub.(Fi.F.ALLOW) ≈0.73(θ.sub.PF /L)GD.sub.MAX (4.0)

    τ.sub.(Gr.F.ALLOW) ≈2.65τ.sub.(Fi.F.ALLOW) (5.0)

    θ.sub.PG ≈1.33θ.sub.PF                 (6.0)

wherein:

τ.sub.(GR.F.ALLOW) is the maximum fatigue allowable shear stress forcomposite graphite material;

τ.sub.(Fi.F.ALLOW) is the maximum fatigue allowable shear stress forcomposite fiberglass material;

θ_(PG) is the pitch prorate for graphite composite material;

θ_(PF) is the pitch prorate for fiberglass composite material;

G is the torsional shear moduli, i.e., about the longitudinal axis, ofthe composite materials (approximately equal for graphite and fiberglassmaterials due to the commonality of resin matrices); and

T_(PR) is the pitch region thickness dimension; and

wherein

equations 3.0-6.0 are solved in terms of the Diameter D_(MAX) to providean expression therefor as follows:

Accordingly, for a predefined pitch region thickness dimension T_(PR),the maximum diameter D_(MAX) of the inscribed circle IN_(CIR) may bedetermined. This diameter dimension D_(MAX), in combination with apredefined value of X, determines the critical angle α by defining twopoints, i.e., the lateral edge 54_(E) and the tangency point A'.

In FIG. 6, curves 60 and 70 graphically depict the ratio of the maximuminterlaminar shear stress (at points B) to the maximum in-plane shearstress (at points A) for the baseline pitch region PR_(BL) and theoptimized pitch region PR, respectively. Referring to FIGS. 4-6, theratio of each is plotted as a function of the normalized edge distancei.e., from a lateral surface, 50_(LBL) or 50_(L), to a centroid, C_(BL)or C, of the respective pitch region views. By examination of the curves60, 70 it will be appreciated that the interlaminar shear stresses aremaximum along the lateral surfaces 50_(LBL), 50_(L) corresponding topoints B and rapidly decline to an insignificant value at about 20% ofthe normalized edge distance. Furthermore, by comparative examination,it will be appreciated that maximum interlaminar shear stresses aresubstantially reduced, i.e., from about 0.73 to about 0.38 or, about 73%to about 38% of the maximum in-plane shear stress, when employing thechamfered edge configuration CH_(E) of the optimized pitch region PR.

FIGS. 7a and 7b show an alternate embodiment of the pitch region PRwherein the core laminate 50 includes a central zone 80 of alternatingunidirectional graphite and fiberglass plies, U_(G) and U_(F),respectively, to augment the axial strength of the optimized flexbeam,and consequently, enhance the centrifugal load carrying capabilitythereof. More specifically, the central zone 80 is disposed proximal tothe flapwise and edgewise bending neutral axis X_(A), Y_(A) so as tominimize its contribution to the bending stiffness of the optimizedflexbeam, and particularly, to the chordwise stiffness thereof.Preferably, the individual unidirectional graphite plies U_(G) aredisposed in staggered relation, shifted laterally with respect to eachother, or, alternatively, staggered in width dimension so as to obviatecoincident alignment of the ply edges. Such staggered arrangementincreases the strength of the core laminate 50 by avoiding localizedstress concentrations which result from chordwise alignment of theindividual graphite plies U_(G).

In FIG. 8, a schematic partially sectioned side view of the optimizedflexbeam 10 is depicted for illustrating the composite ply lay-up andthickness variation therein. For ease of illustration, only the upperhalf of the optimized flexbeam 10 is shown, i.e., from a mid-planethereof, insofar as the lower half is essentially identical.Accordingly, references to the thickness dimensions should be viewed asbeing twice (i.e., 2×) the actual dimensions shown. Furthermore, thespace between solid lines is indicative of unidirectional compositematerial U, and the space between solid and dashed lines is indicativeof off-axis composite material O.

The unidirectional composite material U, i.e., the fiberglass andgraphite plies U_(F), U_(G), of the face and core laminates 50, 52,extend the full length L of the pitch region PR (see FIG. 2b) and,preferably, extend the full spanwise length L_(F) of the optimizedcomposite flexbeam 10. In the described embodiment, these plies U areinterleaved with additional unidirectional and off-axis material, O andU, respectively, in the adjacent regions to effect the requisitethickness transition in the inboard and outboard transition regions ITR,OTR.

In FIGS. 8, 9a and 9b, the inboard transition region ITR effects a widthand thickness transition between the hub attachment region HAR and thepitch region PR. Such width and thickness transitions are typicallydictated by (i) the low torsional stiffness and 1st chordwise frequencyrequirements of the pitch region PR and (ii) the load transferrequirements of the hub attachment region HAR. With regard to theformer, the stiffness and frequency requirements of the pitch region PR,in the main, necessitate that the pitch region width and thicknessdimensions W_(PR), T_(PR) be minimized to reduce the torsional stiffness(1/3W_(PR) T_(PR) ³ *G) and the edgewise bending stiffness (1/12W_(PR) ³T_(PR) * E) of the pitch region PR. And, regarding the latter, therequirement of the hub attachment region HAR to transfer all flexbeamloads via differential bending across the connecting bolts necessitatesthat predefined minimum edge distances be maintained, i.e., for themounting apertures 40 of the hub attachment region HAR to a free edgethereof. As such, the thickness T_(HAR), and, particularly the widthdimension W_(HAR) of the hub attachment region HAR, are typically largerthan the comparable dimensions W_(PR), T_(PR) of the pitch region PR. Inthe described embodiment, a 58% width transition, i.e., from 3.8 in (9.7cm) to 6.0 in (15.2 cm) and a 503% thickness transition, i.e., from0.234 in (0.59 cm) to 1.410 in (3.58 cm), is effected from the pitchregion PR to the hub attachment region HAR.

To more accurately define its configuration and function, the inboardtransition region ITR is subdivided into various subregions includingfirst and second transition subregions ITR-1 and ITR-2, respectively.The first transition subregion ITR-1, effects a thickness transitionwhile the second transition subregion ITR-2 effects both a width andthickness transition. The first transition subregion ITR-1 ismulti-functional insofar as it accommodates thrust-induced flapwisedisplacement, reacts flapwise and edgewise bending loads, and shares aportion of the pitch displacement of the optimized flexbeam (albeitsmall compared to the pitch region PR). The functionality thereof iseffected by the gradual addition of unidirectional composite material U,having a constant width (equal to the width dimension W_(PR) of thepitch region PR) so as to increase the thickness of the flexbeam 10without appreciably increasing the torsional and edgewise stiffnessthereof. Accordingly, the gradual thickness transition accommodatesflapwise displacement while increasing the flapwise bending stiffness toreact the imposed bending loads. Furthermore, the unidirectionalorientation of the composite material U, in combination with the widthconstraint, permits a small degree of pitch motion, thereby reducing thetwist rate requirements of the pitch region PR. For the describedembodiment, the unidirectional composite material U comprises aplurality of unidirectional graphite plies U_(G), which are interleavedwith the unidirectional graphite and fiberglass plies U_(G), U_(F) ofthe pitch region PR.

The second transition subregion ITR-2 is principally designed forreacting flapwise and edgewise bending loads and accommodating thethrust-induced flapwise displacement of the tail rotor blade. Inaddition to these functional requirements, the second transitionsubregion ITR-2 reduces the interlaminar shear stresses along the freeedges of the optimized composite flexbeam. More specifically, the secondtransition subregion ITR-2 defines lateral surfaces, 90_(L) each havinga substantially conic shape. The conic shape may take a variety of formsincluding parabolic, hyperbolic, elliptical or circular curve shapes.With respect to either of the lateral surfaces 90_(L), the conic shape,hereinafter referred to as the "width conic", is initiated at a pointA_(L) corresponding to the juncture of the first and second transitionsubregions ITR-1, ITR-2 and terminates at a point B_(L), correspondingto the juncture of the second transition subregion ITR-2 and the hubattachment region HAR. Furthermore, and referring to FIG. 9b, the widthconic defines conic slope angle θ_(WC) at various points therealong andis given by a standard transcendental function:

    θ.sub.WC =Tan-1(DY/DX)

wherein DY/DX is the width conic slope at a particular point relative toan X-Y-coordinate system. The X-axis thereof is parallel to thelongitudinal axis (not shown in FIG. 9b) of the optimized flexbeam 10and the Y-axis intersects point A_(L) of the width conic. The slopeangle θ_(WC) of the width conic at point A_(L) is 0 degrees andincreases to between about 30 to about 50 degrees at the terminal pointB_(L).

The inventors discovered that interlaminar shear stresses aresignificant reduced by introducing off-axis composite material O, incombination with unidirectional composite material U, as a function ofthe conic slope angle θ_(WC). The relationship is independent of thefiber composition, i.e., graphite or fiberglass, though, for thedescribed embodiment, a combination of off-axis graphite and fiberglassplies O_(G), O_(F), are employed to alleviate thermally inducedstresses. Such stresses may develop as a result of a thermal mismatchduring cure operations, between unidirectional fiberglass and graphiteplies U_(F) U_(G) and off-axis graphite plies O_(G). Accordingly, it maybe desirable to introduce off-axis fiberglass plies OF therebetween,which off-axis fiberglass plies U_(F) are characterized by a thermalexpansion coefficient which is more compatible with the unidirectionalplies U_(F), U_(G) and the off-axis graphite plies O_(G).

Before defining the relationship, it should be appreciated that thepercentage of off-axis material O must increase by at least 50% from thepitch transition region PR to the hub attachment region HAR. Thispercentage increase is necessary inasmuch as the pitch region PR, asdiscussed hereinabove, is comprised solely of unidirectional compositematerial U while the hub attachment region requires a 50/50 admixture ofoff-axis and unidirectional materials O, U for optimally transferringloads through the bolted attachment. Furthermore, while the build-up ofoff-axis composite material O is initiated in the first transitionsubregion ITR-1 and is maximum, i.e., 50%, in the second transitionsubregion ITR-2, the prescribed percentage is most critical in areasCR_(wt) corresponding to shallow angles θ_(WC) of conic slope, i.e.,between about 0 degrees to about 10 degrees of conic slope. This areaCR_(wt), which corresponds to the outboard portion of the secondtransition subregion ITR-2, is hereinafter referred to as the criticalwidth transition subregion CR_(wt).

In FIG. 10, an optimized curve 100 having upper and lower limitboundaries 100_(U) and 100_(L) defines the percentage O% of off-axiscomposite material O, i.e., percentage of the total off-axis pliesO_(G), O_(F) to the total material composition at a given cross-sectionas a function of the conic slope angle θ_(WC). The optimized curve 100is defined for slope angles θ_(WC) between 0 and 10 degrees wherein theinterlaminar shear stresses developed in the critical transitionsubregion CR_(wt) are highest. While the build-up of off-axis compositematerial O outboard and inboard of the critical width transitionsubregion is less critical, such build-up is preferably gradual to avoidhigh axial strains which are geometrically induced, i.e., caused byabrupt contour changes.

The optimized curve 100 is defined by the expression: ##EQU1## whereinthe constant C is between about 14.4 to about 21.6 and defines the rangeof Y-intercept values of the optimized curve 100, wherein the slopeangle θ_(WC) is in degrees, and wherein the constant k is equal to 1.0degrees⁻¹ to provide consistency of units in the expression. It will beapparent from the expression that the constant C also defines the upperand lower limit boundaries 100_(U) and 100_(L) of the optimized curve100.

From the expression it will be appreciated that the percentage %O ofoff-axis composite material O, corresponding to zero slope is betweenabout 14.4% to about 21.6% and is about 35.4% to about 42.6% at 10degrees of conic slope. The build-up of off-axis composite material Onecessary to effect such percentage in the critical transition subregionCR_(wt) i.e., at the Y-intercept of the optimized curve 100, isinitiated in the first transition subregion ITR-1 at a radially outboardspanwise position I_(BU) (see FIG. 9a). Preferably, the spanwiseposition I_(BU) corresponds to a dimension D_(S) from the junction ofthe first and second transition subregions ITR-1, ITR-2, which dimensionD_(S) is about 15% to about 25% of the spanwise length L₁ of the firsttransition subregion ITR-1. This position I_(BU) ensures that the twistrate is not adversely affected and that the off-axis material O may begradually increased to effect the minimum off-axis material O in thecritical transition subregion CR_(wt). The build-up of off-axiscomposite material O beyond the critical transition subregion CR_(wt),i.e., inboard thereof, may be more rapid insofar as interlaminar shearstresses are relatively benign and, consequently, the precise thicknesstransition therein is less critical. While the optimized curve 100 andits limit boundaries 100_(U) and 100_(L) are depicted as smoothcurvilinear functions, it should be understood that, in practice, thecurve 100 will be a stepped function due to the incremental thicknessbuild-up of individual off-axis plies O_(G), O_(F).

In FIG. 11, a prior art flexbeam 110, is shown in phantom and overlayingthe optimized composite flexbeam 10 of the present invention forillustrating the benefits derived from the configuration andconstruction of the inboard transition region ITR. The prior artflexbeam 110 is characterized by a linear width and thickness transitionregion TR₁₁₀ and a uniform build-up of off-axis composite material. Withregard to the latter, such build-up is typically effected at a spanwiseposition I₁₁₀ which is radially inboard of the initial width transitioncorresponding to point A₁₁₀. Such initial placement of off-axiscomposite material serves to maximize the effective length of the pitchregion PR₁₁₀. By analysis it can be shown that interlaminar shearstresses at point A₁₁₀ of the prior art flexbeam 110 are 2 to 3 timeshigher than the comparable interlaminar shear stresses at point A_(L) ofthe optimized flexbeam 10. Such high stress levels are developed as aresult of the high slope angle and inboard placement of the off-axiscomposite material. As discussed in the Background of the inventionresort has been made to edge caps C₁₁₀ or composite overwraps (notshown) to reduce interlaminar shear stresses to acceptable levels. Theinboard transition region ITR of the optimized flexbeam 10 eliminatesthe weight, cost and complexity of such additional structure by thecombined structural effects of the width conic and the optimizedbuild-up of off-axis composite material. The width conic effects agradual width transition while the off-axis composite material providesthe requisite shear strength to reduce interlaminar shear stresses alongthe lateral surfaces 90_(L) of the second transition subregion ITR-2.

In addition to these structural benefits, the configuration andconstruction of the inboard transition region ITR effects a reduction inthe edgewise and torsional stiffness of the optimized composite flexbeam10 while, concomitantly, increasing the effective length of theregions/subregions responsible for accommodating pitch motion, i.e., thepitch region PR and first transition subregion ITR-1. By comparing themean width dimension W₁₁₀ of the prior art flexbeam 110 to the meanwidth dimension W₁₀ of the optimized flexbeam and the respectivelocations of each, it will be apparent that area and polar moments ofinertia (I and J) are reduced, thereby minimizing the overall edgewiseand torsional stiffness of the optimized flexbeam 10. As such, theinboard transition region ITR permits greater design flexibility withrespect to (i) establishing the desired 1st chordwise frequency of theoptimized flexbeam 10 (ii) reducing control loads required to impartpitch motion to the optimized flexbeam 10 and/or (iii) reducing thelength and/or weight thereof.

To further reduce the edgewise and torsional stiffness of the optimizedflexbeam 10, it may be desirable to locate the width conic as close aspracticable to the mounting apertures 40 of the hub attachment regionHAR such that the width conic continues radially inboard of a thicknessjuncture T_(T) defined by the terminus of the thickness transition. Morespecifically, it is desirable to cause a point C_(L) disposed along thewidth conic to be within an S/D_(A) range of about 1.60 to about 1.85wherein S is the distance from the point C_(L) to the geometric center40_(C) of the nearest mounting aperture 40 and D_(A) is the diameter ofthe respective mounting aperture 40. As such, the spatial position ofthe width conic may be shifted inwardly toward the mounting apertures40, thereby causing the mean width dimension W₁₀ to be positioned at aninboardmost radial location.

In FIG. 12, the outboard transition region OTR accommodates a width andthickness transition between the pitch region PR and the bladeattachment region BAR. The outboard transition region OTR is principallydesigned for reacting centrifugal loads and may be characterized aslightly-loaded in comparison to the inboard transition region. That is,loads acting on the outboard transition region OTR are about 1/3rd ofthose acting on the inboard transition region. Insofar as the loads areless demanding, the width and thickness transitions can occur rapidlywithout inducing high interlaminar shear stresses. In the describedembodiment, off-axis graphite plies O_(G) are disposed in interleavedcombination with the unidirectional fiberglass and graphite plies U_(F),U_(G) of the pitch region so as to effect a rapid, conic-shapedthickness transition. Furthermore, sufficient off-axis graphite pliesO_(G) are introduced to effect a 50/50 admixture of unidirectional andoff-axis composite material U, O in the blade attachment region BAR.

In FIG. 13 the outboard transition region is characterized by many ofthe same features of the inboard transition region ITR. For example, thelateral surfaces 120_(L) of the outboard transition region OTR define aconic shape which are disposed in close proximity to the mountingapertures 42 of the blade attachment region BAR, i.e., inboard of thethickness juncture T_(T). As discussed earlier, these features, interalia, increase the effective length of the pitch region PR, reduceinterlaminar shear stresses and reduce weight.

The optimized composite flexbeam 10 of the present invention may bemanufactured by conventional manufacturing techniques including vacuumforming, press molding and resin transfer molding. In the preferredembodiment, a vacuum forming process is employed for curing thecomposite material U, O of the optimized flexbeam. More specifically,and referring to FIGS. 14 and 15, a composite lay-up CL is produced byplacing, i.e., either by hand or via a numerically controlled tapelay-up head, uncured plies of resin impregnated unidirectional andoff-axis composite material in a base metal mold 140 which defines aface surface 142 of the optimized flexbeam 10. Furthermore, theunidirectional and off-axis material is laid so as to define thethickness dimensions of the optimized composite flexbeam. The widthdimension W_(CL) is initially oversized relative to the final net shapedflexbeam 10, and, preferably, the width dimension W_(CL) is oversized byabout 30% to about 50% relative to the width dimension W_(HAR) of hubattachment region.

A semi-rigid caul 144 (see FIG. 15) is disposed over the exposed uppersurface CL_(S) of the composite lay-up CL and an impervious flexiblemembrane 146, commonly referred to as the vacuum bag, is disposed overthe caul 144 and sealed to the base mold 140. A vacuum source 148evacuates the mold cavity occupied by the composite lay-up CL such thatthe vacuum bag and semi-rigid caul compact the lay-up CL in preparationfor autoclave curing. The entire mold assembly 150 is placed inautoclave (not shown) wherein heat and additional pressure is applied tothe lay-up CL for curing the composite lay-up CL.

Insofar as the composite lay-up CL is essentially planar, compactionpressure P may be uniformly applied thereto without requiringbi-directional pressure components, e.g., pressure in both the lateraland transverse directions. As discussed in the Background of theInvention, the prior art cruciform configuration requires bi-directionalpressure to form the face and lateral surfaces of the structural rib.Furthermore, the vacuum forming process, and, more particularly, thesemi-rigid caul 144, is forgiving of fiber bulk variations therebydistributing pressure within the composite lay-up CL and improving thequality of the resulting laminate.

The cured composite lay-up CL is formed to net width dimensions usingconventional cutting apparatus such as a high speed, multi-axis millingmachine. The final forming step includes milling the edges of theoptimized flexbeam to produce the chamfered edge surfaces describedabove. While the chamfered edge surfaces may be limited to the length ofthe pitch region, the chamfered edge surfaces may extend into adjacentregions to facilitate manufacturing and obviate stresses due to abruptcontour changes.

While the preferred embodiment of the optimized flexbeam 10 incorporatesvarious regions and subregions in combination, it will be appreciatedthat the specific teaching of a single region, e.g., the pitch is regionPR or the inboard transition region ITR, may be applied to otherflexbeam configurations. That is, the teachings associated with oneregion may be used in combination with other regions having aconventional configuration such as those taught in the prior art orhaving modified configurations to suit a particular application. Forexample, the pitch region PR may be used in combination withconventional inboard and outboard transition regions having a linearwidth transition and/or a linear build-up of off-axis material.Likewise, the inboard transition region ITR may be used in combinationwith a pitch region having a right-angled edge configuration and/or asingle material composite laminate, e.g., all unidirectional graphite orall unidirectional fiberglass material. Furthermore, the inboard and/oroutboard transition regions ITR, OTR may be used in combination with ahub attachment region and/or blade attachment region, respectively,having a non-constant width and thickness dimension so as to becompatible with other hub or blade attachment arrangements.

Although the invention has been shown and described with respect toexemplary embodiments thereof, it should be understood by those skilledin the art that the foregoing and other changes, omissions and additionsmay be made therein and thereto, without departing from the spirit andscope of the present invention.

What is claimed is:
 1. An optimized composite flexbeam (10) for ahelicopter tail rotor assembly (2), the optimized composite flexbeam(10) having a plurality of adjoining regions including a hub attachmentregion (HAR), a blade attachment region (BAR), an inboard transitionregion (ITR) adjoining the hub attachment region (HAR), and an outboardtransition region (OTR) adjoining the blade attachment region (BAR), theoptimized composite flexbeam (10) further comprising:a pitch region (PR)adjoining the inboard and outboard transition regions (ITR, OTR) anddefining a flapwise bending neutral axis (X_(A)), said pitch region (PR)including: a core laminate (50) of unidirectional fiberglass material(U_(F)), said core laminate (50) defining lateral surfaces (50_(L) ) andmating surfaces (50_(M)), said lateral surfaces (50_(L) ) defining apitch region width dimension (W_(PR)) therebetween; face laminates (52)of unidirectional graphite material (U_(G)), said face laminates (52)being bonded to said mating surfaces (50_(M)) of said core laminate(50),said face laminates(52), furthermore, defining face surfaces (52_(F)),said face surfaces (52_(F)) defining a pitch region thickness (T_(PR))dimension therebetween; said pitch region width and thickness dimensions(W_(PR), T_(PR)) defining an aspect ratio, said aspect ratio beinggreater than or equal to 10; said core and face laminates (50, 52),furthermore, defining a chamfered edge configuration (CH_(E)) havingchamfered edge surfaces (54_(S)), each said chamfered edge surface(54_(S)) defining a critical acute angle α with respect to said flapwisebending neutral axis (X_(A)), and, furthermore, defining a lateral edge(54_(E)) disposed a vertical distance X from said flapwise bendingneutral axis (X_(A)); said critical acute angle α being between about 14degrees to about 22 degrees; said vertical distance X being about 12.5%to about 37.5% of said pitch region thickness dimension T_(PR).
 2. Theoptimized composite flexbeam (10) according to claim 1 wherein saidaspect ratio is between about 10 to about
 20. 3. The optimized compositeflexbeam (10) according to claim 1 wherein said critical acute angle αis between about 16 degrees to about 20 degrees.
 4. The optimizedcomposite flexbeam (10) according to claim 1 wherein said unidirectionalfiberglass and graphite materials (U_(F), U_(G)) each have a shearmodulus, said shear moduli of said unidirectional fiberglass andgraphite materials (U_(F), U_(G)) being substantially equal.
 5. Theoptimized composite flexbeam (10) according to claim 4 wherein saidmating surfaces (50_(M)) of said core laminate (50) define a corethickness dimension (T_(C)), said core thickness dimension (T_(C)) beingwithin a range of about 50% to about 70% of said pitch region thicknessdimension (T_(PR)).
 6. The optimized composite flexbeam (10) accordingto claim 1 wherein said pitch region (PR) further includes a centralzone (80) of alternating unidirectional fiberglass and graphite plies(U_(F), U_(G)).
 7. The optimized composite flexbeam (10) according toclaim 6 wherein said unidirectional graphite plies (U_(G)) are disposedin staggered relation.
 8. The optimized composite flexbeam (10)according to claim 1 wherein said chamfered edge surfaces (54_(S))extend into the inboard and outboard attachment regions (ITR, OTR). 9.An optimized composite flexbeam (10) for a helicopter tail rotorassembly (2), the optimized composite flexbeam (10) having a pluralityof adjoining regions including a hub attachment region (HAR), a bladeattachment region (BAR), and an outboard transition region (OTR)adjoining the blade attachment region (BAR), the optimized compositeflexbeam (10) further comprising:an inboard transition region (ITR)adjoining the hub attachment region (HAR) and having a combination ofunidirectional and off-axis composite materials (U, O) defining a totalmaterial composition and a percent %O of off-axis composite material (O)relative thereto, said inboard transition region (ITR) furtherincluding: a first transition subregion (ITR-1) defined by a thicknesstransition; and a second transition subregion (ITR-2) defined by a widthand thickness transition and defining a width conic, said secondtransition subregion (ITR-2) defining a critical width transitionsubregion (CR_(wt)); said width conic defining conic slope angles θ_(WC); said critical width transition subregion (CR_(wt)) corresponding toconic slope angles θ_(WC) between 0 degrees to about 10 degrees; saidpercent %O of off-axis composite material (O) defined by an optimizedcurve (100), said optimized curve (100) in said critical transitionsubregion subregion (CR_(wt)) being defined by the expression: ##EQU2##wherein C is a constant between about 14.4 to about 21.6, and k is aconstant equal to 1.0 degrees⁻¹ ; a pitch region (PR) adjoining theinboard and outboard transition regions (ITR, OTR) and defining aflapwise bending neutral axis (X_(A)), said pitch region (PR) including:a core laminate (50) of unidirectional fiberglass material (U_(F)), saidcore laminate (50) defining lateral surfaces (50_(L)) and matingsurfaces (50_(M)), said lateral surfaces (50_(L)) defining a pitchregion width dimension (W_(PR)) therebetween; face laminates (52) ofunidirectional graphite material (U_(G)), said face laminates (52) beingbonded to said mating surfaces (50_(M)) of said core laminate (50), saidface laminates (52), furthermore, defining face surfaces (52_(F)), saidface surfaces (52_(F)) defining a pitch region thickness (T_(PR))dimension therebetween; said pitch region width and thickness dimensions(W_(PR),T_(PR)) defining an aspect ratio, said aspect ratio beinggreater than or equal to 10; said core and face laminates (50, 52),furthermore, defining chamfered edge configuration (CH_(E)) havingchamfered edge surfaces (54_(S)), each said chamfered edge surface(54_(S)) defining a critical acute angle α with respect to said flapwisebending neutral axis (X_(A)), and, furthermore, defining a lateral edge(54_(E)) disposed a vertical distance X from said flapwise bendingneutral axis (X_(A)); said critical acute angle α being between about 14degrees to about 22 degrees; said vertical distance X being about 12.5%to about 37.5% of said pitch region thickness dimension (T_(PR)). 10.The optimized composite flexbeam (10) according to claim 9 wherein saidfirst transition subregion (ITR-1) and said second transition subregion(ITR-2) define a juncture therebetween, wherein said first transitionsubregion (ITR-1) defines a spanwise length dimension (L₁) and aspanwise position (I_(BU)) defining an initial build-up of said off-axiscomposite material (O), said spanwise position (I_(BU)) being radiallyoutboard of said juncture.
 11. The optimized composite flexbeam (10)according to claim 10 wherein said spanwise position (I_(BU)) isdisposed a distance (D_(S)) from said juncture, said distance (D_(S))being between about 15% to about 25% of said spanwise length dimension(L₁).
 12. The optimized composite flexbeam (10) according to claim 9wherein said second transition subregion (ITR-2) defines thicknessjuncture (T_(T)), and wherein said width conic continues radiallyinboard of said thickness juncture (T_(T)).
 13. The optimized compositeflexbeam (10) according to claim 12 wherein said hub attachment region(HAR) defines a mounting aperture (40) having a diameter dimension(D_(A)) and a geometric center (40_(C)), and wherein said width conicdefines a point C_(L) disposed therealong, said point (C_(L)) defining adistance dimension S from said geometric center (40_(C)), said distanceand diameter dimensions S, D defining an S/D ratio, said S/D ratio beingbetween about 1.60 to about 1.85.
 14. The optimized composite flexbeam(10) according to claim 9 wherein said aspect ratio is between about 10to about
 20. 15. The optimized composite flexbeam (10) according toclaim 9 wherein said critical acute angle α is between about 16 degreesto about 20 degrees.
 16. The optimized composite flexbeam (10) accordingto claim 9 wherein said unidirectional fiberglass and graphite materials(U_(F), U_(G)) each have a shear modulus, said shear moduli of saidunidirectional fiberglass and graphite materials (U_(F), U_(G)) beingsubstantially equal.
 17. The optimized composite flexbeam (10) accordingto claim 16 wherein said mating surfaces (50_(M)) of said core laminate(50) define a core thickness dimension (T_(C)), said core thicknessdimension (T_(C)) being within a range of about 50% to about 70% of saidpitch region thickness dimension (T_(PR)).
 18. The optimized compositeflexbeam (10) according to claim 9 wherein said pitch region (PR)further includes a central zone (80) of alternating unidirectionalfiberglass and graphite plies (U_(F), U_(G)).
 19. The optimizedcomposite flexbeam (10) according to claim 18 wherein saidunidirectional graphite plies (U_(G)) are disposed in staggeredrelation.
 20. The optimized composite flexbeam (10) according to claim 1wherein said chamfered edge surfaces (54_(S)) extend into the inboardand outboard attachment regions (ITR, OTR).